We obtain a $(p,\nu)$-extension of Srivastava's triple hypergeometric function $H_C(\cdot)$ by employing the extended Beta functioninebreak $B_{p,\nu}(x,y)$ introduced in Parmar et al.~[J. Class. Anal. extbf{11} (2017), 91--106]. We give some of the main properties of this extended function, which include several integral representations, the Mellin transform, a differential formula, recursion formulas and a bounded inequality.